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On potentials of Itô's processes with drift in L_d+1

2021/02/21 by Krylov, N. V.
#60H10 #60J60 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2102.10694

Abstract

This paper is a natural continuation of \citeKr₂0₂, where strong Markov processes are constructed in time inhomogeneous setting with Borel measurable uniformly bounded and uniformly nondegenerate diffusion and drift in L_d+1(ℝ^d+1). Here we study some properties of these processes such as the probability to pass through narrow tubes, higher summability of Green's functions, and so on. The results seem to be new even if the diffusion is constant.

Some properties of solutions of Itô equations with drift in L_d+1
On diffusion processes with drift in L_d+1
On time inhomogeneous stochastic Itô equations with drift in L_d+1
On diffusion processes with drift in a Morrey class containing L_d+2
On stochastic equations with drift in L_d

On potentials of Itô's processes with drift in Ld+1

Abstract

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On potentials of Itô's processes with drift in L_d+1